Ellipses and Hyperbolas with the Same Focal Points
This Demonstration shows that ellipses and hyperbolas with the same focal points (here placed at the points external image 1.gif and external image 2.gif) always cross each other orthogonally.
The variables used for the curves are the eccentricities, external image 3.giffor the ellipses andexternal image 4.gif for the hyperbolas.
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So when I move e1, the cycle will become bigger or smaller, but the minum radius is from X1 to X-1.
When we move e2, the two line will became outside or inside.
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This is the picture after we move it, we can see how different between every moved. Also this is the minum or maxnum of e1 and e2.